Q. An Infantry unit is attacked and forced to retreat onto a frozen river. It has one figure left. Two dice are rolled. a Star comes up and the Infantry figure is eliminated. Does this count as a medal for the opponent?
A. Yes. When rolling for units moving or retreating onto a frozen river, we have the opposition player roll to see if the ice is thin and figures are lost. Note: Frozen rivers are the only terrain where its effect is still applied when a unit retreats onto it.

Q. When a unit is already on a frozen river hex, does it need to roll if it does not move?
A. No

Q. An Infantry unit is attacked and forced to retreat onto a frozen river. It has one figure left. Two dice are rolled. a Star comes up and the Infantry figure is eliminated. Does this count as a medal for the opponent?
A. Yes. When rolling for units moving or retreating onto a frozen river, we have the opposition player roll to see if the ice is thin and figures are lost. Note: Frozen rivers are the only terrain where its effect is still applied when a unit retreats onto it.

I missed this in the FAQ -- which I did check before I posted my question, but not well enough I guess

So, it looks like the official answer is that the opposing player makes those frozen river rolls.